Mathematical Finance with MATLAB©
DOI:
https://doi.org/10.46661/revmetodoscuanteconempresa.2067Keywords:
MATLAB, Ibex 35, valoración de opciones, componentes principales, ecuaciones de Black-Scholes, método Monte Carlo, método binomial, options valuation, principal components, Black-Scholes equations, Monte Carlo method, binomial methodAbstract
The aim of this paper is to present the MATLAB tools for the teaching and the applications in the Mathematical Finance. This paper has two parts; the first one is a statistical study of the movement of the prices for the securities in the Ibex 35 during the year 2006. The second one is about the different procedures: the Black-Scholes equation, Monte-Carlo method and Binomial method, to calculate the prices of financial options.
Downloads
References
L. Bachelier, Theorie de la speculation, Annales de l’École Normale Superieure (1900), no. 17, 21–86.
F. Blach and M. Scholes, The Princing of Options and Corporate Liabilities, Journal of Political Economy (1973), no. 81, 637–59.
L. Boltzmann, Über die mechanische Bedeutung des Zweiten Haupsatzes der Wärmetheorie, Wien. Ber. (1866), no. 53, 195–220.
L. Boltzmann, Studien über das Gleichgewichtder lebendigen Kraft zwischen bewegten materiellen Punkten, Wien. Ber. (1868), no. 58, 517–560.
L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen, Wien. Ber. (1872), no. 66, 275–370.
R. Brown, A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies, Phil. Mag. (1828), no. 4, 161–173.
J.C. Cox, S.A. Ross, and M. Rubinstein, Option princing: a simplied approach, Journal of Financial Economics (1979), no. 7, 229–263.
B. del Hoyo and F. Vadillo, Sobre la enseñanza del Análisis Numérico, Boletin de la Sociedad Española de Matemática Aplicada (2005), no. 33, 13–18.
A. Einstein, Folgerungen aus den Capillaritätserscheinungen, Ann. Phys. (Leipzig) (1901), no. 4, 513–523.
B.S. Everitt, The Cambridge Dictionary of Stastistic, 3th edn, Cambridge Unersity Press, 2006.
P. Glasserman, Monte Carlo Methods in Financial Enginnering, Springer, 2004.
D.J. Higham, An Introduction to Financial Option Valuation, SIAM, 2000.
D.J. Higham and N.J. Higham, MATLAB Guide, SIAM, 2000.
D.J. Higham and P.E. Kloeden, Maple and Matlab for E.D.E. in Finance, disponible en: www.maths.strath.ac.uk.
H. Hotelling, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol. (1933), no. 24, 417–441, 498–520.
H. Hotelling, Simplified calculation of principal components, Psychometrika (1936), no. 1, 27–35.
J. Hull, Introducción a los mercados de futuros y opciones, Prentice Hall, 1996.
J. Hull, Options, Futures and Others Derivatives, 4th edn, Prentice Hall, 2000.
E. Mach, Die Principien der Wärmelehre: Historisch-kritisch entwickelt, Leipzig, Johann Ambrosius Barth, 1896.
E. Mach, Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen, Physikalische Zeitschrift (1910), no. 11, 599–606.
J. C. Maxwell, On the Dynamical Theory of Gases, Philosophical Transactions (1866), no. CLVII, 49–88.
R.C. Merton, Theory of rational option pricing, Bell Journal of Economics an Mangement Science (1973), no. 4, 141–183.
N. Metropolis, The Beginning of the Monte Carlo Method, Los Alamos Science (1987), no. 15, 125–130.
N. Metropolis and S. Ulam, The Monte Carlo method, J. of the American Statistical Association (1949), no. 44, 335–341.
C.B. Moler, MATLAB- an interactive matrix laboratory, University of New Mexico, Mathematics Department, Report 369 (1979).
C.B. Moler, Numerical Computing with MATLAB, SIAM, 2004.
W. Ostwald, Vorlesungen über Naturphilosophie, Leipzig, Johann Ambrosius Barth, 1901.
K. Pearson, On lines and planes of closest fit to system of points in space, Philos. Mag. (1901), no. 2, 559–572.
S.R. Ross, An Introduction to Mathematicl Finance, Cambrige University Press, 1999.
R. Seydel, Tools for Computational Finance. Third Edition, Springer, 2006.
S. Ulam, R.D. Richtmyer, and J. von Neumann, Statistical methods in neutron diffusion, Los Alamos Scientific Laboratory report LAMS-551 (1947).
N. Wiener, The mean of a functional of arbitrary elements, Ann. of Math. (1920), no. 22, 66–72.
N. Wiener, The average of an analytical functional and the Brownian movement, Proc. Nat. Acad. Sci. USA (1921), no. 7, 294–298.
P. Wilmont, Introduction Quantitative Finance, John Wiley & Sons, 2001.
P. Wilmont, S. Howison, and J. Dewynne, The Mathematic of Financial Derivatives. Un Student Introduction, Cambridge Univesity Press, 1995.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2007 Revista de Métodos Cuantitativos para la Economía y la Empresa
![Creative Commons License](http://i.creativecommons.org/l/by-sa/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Submission of manuscripts implies that the work described has not been published before (except in the form of an abstract or as part of thesis), that it is not under consideration for publication elsewhere and that, in case of acceptance, the authors agree to automatic transfer of the copyright to the Journal for its publication and dissemination. Authors retain the authors' right to use and share the article according to a personal or instutional use or scholarly sharing purposes; in addition, they retain patent, trademark and other intellectual property rights (including research data).
All the articles are published in the Journal under the Creative Commons license CC-BY-SA (Attribution-ShareAlike). It is allowed a commercial use of the work (always including the author attribution) and other derivative works, which must be released under the same license as the original work.
Up to Volume 21, this Journal has been licensing the articles under the Creative Commons license CC-BY-SA 3.0 ES. Starting from Volume 22, the Creative Commons license CC-BY-SA 4.0 is used.